Study Notes for FIN 340: Capital Structure Basics and MM-Theorem

FIN 340 Intermediate Financial Management: Capital Structure Basics and MM-Theorem

Topic Outline

  1. Idea of Optimal Capital Structure

  2. How to Change Capital Structure

  3. The Effect of Financial Leverage on Cash Flows and the Cost of Equity

  4. Homemade Leverage and MM Theorem with No Taxes

    • Proposition I: Value of the unlevered and levered firm

    • Proposition II: Cost of equity of the unlevered and levered firm

  5. MM Theorem with Taxes

    • Proposition I

    • Proposition II

1. What is Optimal Capital Structure?

The primary goal of financial managers is to maximize stockholder wealth. This involves selecting a capital structure that will achieve that goal. The optimal capital structure is defined as the capital structure that maximizes stockholder wealth, which can be achieved either by maximizing the value of the firm or by minimizing the cost of capital (i.e., the weighted average cost of capital, WACC). The key decision revolves around choosing between debt financing and equity financing.

2. How to Change Capital Structure?

Changing capital structure is often referred to as capital restructuring and involves maintaining the firm's assets while altering its financial leverage.

  • Increasing leverage can be done by issuing debt and repurchasing outstanding shares.

  • Decreasing leverage involves issuing new shares and retiring outstanding debt; this process is also known as recapitalization.
    The following changes occur:

  • Increase in Debt leads to a decrease in Equity.

  • Conversely, an increase in Equity leads to a decrease in Debt.

Capital Restructuring Illustration

Balance Sheet (simplified)

  • Assets: Current and Fixed Assets

  • Liabilities and Shareholders’ Equity: Current Liabilities (Accounts Payable, Notes Payable), Long-term Debt, Owner’s Equity (Common Stock, Retained Earnings)

Recapitalization Example

In a scenario where the total capital is $100 million, with debt and equity both at $50 million, if the company aims for a debt-to-equity (D/E) ratio of 0.2, the following calculations are relevant:

  • Debt/Capital Ratio:
    D/Capital=DD+E\text{D/Capital} = \frac{D}{D + E}
    Assuming D = 0.2 and E = 1, it leads to an ending debt of:
    Ending Debt=(DCapital)×Total Capital=100M×0.167=16.7M\text{Ending Debt} = \left(\frac{D}{\text{Capital}}\right) \times \text{Total Capital} = 100M \times 0.167 = 16.7M

  • The change in debt (∆D) is calculated as follows:
    ΔD=Ending Debt−Beginning Debt=16.7M−50M=−33.3M\Delta D = \text{Ending Debt} - \text{Beginning Debt} = 16.7M - 50M = -33.3M
    This indicates that the reduction in debt, entirely financed through issuance of equity, leads to equity issuance amounting to $33.3 million.

3. The Effect of Leverage

Financial leverage affects a firm's earnings per share (EPS) and return on equity (ROE). An increase in debt financing leads to an increase in fixed interest expenses.

  • In good years, excess earnings are available for shareholders.

  • In poor years, fixed expenses remain, thus leaving less for shareholders.
    Therefore, leverage magnifies the variations in both EPS and ROE, and consequently increases costs of equity due to heightened risk associated with leveraged equity.

Example: Financial Leverage, EPS, and ROE

Ignoring tax implications initially: We consider the firm's condition with no debt financing.

  • Current Scenario: Assets at $5 million, debt at $0, equity at $5 million, debt/equity ratio of 0, and share price at $10 (500,000 shares).

  • Financial Results Based on various states (Recession, Expected, Expansion):

    • EBIT of $300,000, $650,000, $1,000,000 yields net income and corresponding ROE and EPS figures as follows:

    • Recession: Net Income $300,000, ROE 6%, EPS $0.60

    • Expected: Net Income $650,000, ROE 13%, EPS $1.30

    • Expansion: Net Income $1,000,000, ROE 20%, EPS $2.00

Proposed Structure

In the proposed structure, half of the capital is financed by debt and half by equity. Here, the asset value is unchanged, and total capital remains at $5 million, with a new debt/equity ratio of 1.

  • Interest payments, in this case, provide a varied outcome for net incomes in different states and illustrate the variation in ROE and EPS under a leveraged structure (resulting in lower ROE and EPS in recessionary conditions and amplified returns in expansion conditions).

4. Assumptions of the M&M Model

  • Perpetual Cash Flows: Continuous cash streams without defined ends.

  • Perfect Capital Markets: All parties have equal access to information and ability to borrow/lend at the same rate, no transaction costs, and absence of taxes.

5. Effect of Capital Structure on Firm Value

An example evaluation compares Firm A (all-equity) vs. Firm B (40% debt).

  • Firm A: Market Cap $2,000, Net Income varies by economic state (Recession: $100, Expected: $200, Expansion: $300).

  • Firm B: Market Cap $1,200, Debt valued at $800 with an interest rate of 8%.
    Various financial strategies highlight differences in investment opportunities presented through respective market capitals and leverage, scrutinizing potential arbitrage.

Homemade Leverage Strategy

An investor exploring homemade leverage by borrowing to engage with Firm A can replicate payouts similar to those received when investing in Firm B.

MM Proposition I (No Taxes)

The concept posits that capital structure is irrelevant to the firm's value. The equation concludes that the value of a levered firm equals that of an unlevered firm:
V<em>L=V</em>UV<em>L = V</em>U

MM Proposition II (No Taxes)

This proposition conveys that increased leverage raises the risk and potential return for shareholders. The mathematical representation is articulated as:
R<em>s=R</em>0+(BS)(R<em>0−R</em>B)R<em>s = R</em>0 + \left(\frac{B}{S}\right)(R<em>0 - R</em>B)
Where:

  • $R_s$: cost of equity (return on levered equity)

  • $R_B$: cost of debt (interest rate)

  • $R_0$: return on unlevered equity (return on assets)

Example Calculation

For a no-tax scenario, while determining equity’s overall cost under various leverage levels provides insights into funding patterns. For a targeted debt/equity ratio, the cost of capital may markedly shift due to leverage risks.

Capital Structure Theory Summary (with Taxes)

The incorporation of taxes modifies the outcomes related to capital structure, allowing for deductions on interest that creatively shift firm value. The pivotal relations are elucidated through multiple propositions:

  1. MM Proposition I with Taxes:
    V<em>L=V</em>U+TCimesBV<em>L = V</em>U + TC imes B
    The firm's value is enhanced by the present value of the tax shield.

  2. MM Proposition II with Taxes: The return on equity remains influenced, specified by:
    R<em>S=R</em>0+(BS)(R<em>0−R</em>B)(1−TC)R<em>S = R</em>0 + \left(\frac{B}{S}\right)(R<em>0 - R</em>B)(1-T_C)

The overarching principle encapsulates firm value optimization in tax scenarios, emphasizing the interplay between leverage and fiscal strategy in revealing profitability flows and cost efficiencies.